DESCRIPTION: Over the past decade, both multi-center clinical trials and health observational studies have become increasingly conducted in medical research sponsored by the National Institutes of Health. The Food and Drug Administration has recently been promoting the Bayesian initiative in health economics and outcomes research. However, Bayesian study design methodology is limited. The goal of this proposal is to develop statistical Bayesian methods for efficient sample size calculation based on three types of outcome data (continuous data without covariates, binary data with covariates, and continuous data with covariants). We will develop Bayesian hierarchical models in order to assess a particular aspect, e.g., the overall diagnostic accuracy and the mean (or range) of the treatment benefit, across some or all of the participating centers. Both the effects of "individual" (patients) and "clusters" (care providers or clinical centers) are incorporated in our models. The prior knowledge is derived from the literature or assumptions. We first pre-specify criteria such as the average posterior interval length and the target coverage probability of a particular "function" of the parameters. We then create and apply the approximation and direct Markov-chain Monte Carlo simulation approaches to compute the desired sample size. The proposed methodology will be illustrated on subjective and objective risk-assessment analysis for predicting major inhospital complications following percutaneous coronary interventions. The main advantages of the proposed Bayesian approaches are that a substantial sample size could be saved compared with the Non-Bayesian competitors; the prior information is utilized; and the complex data structure and variability are incorporated. Our approach may allow for better evaluation of outcomes (e.g., effectiveness, quality, access, cost of health services). The methodology is applicable to the design of similar health care quality studies.